9.5 Free Energy and Equilibrium

Free Energy and the Reaction Quotient

ΔG = ΔG° + RT ln(Q) relates free energy to how far a reaction has progressed. When Q < K, ΔG is negative (forward reaction favored). When Q > K, ΔG is positive (reverse favored). At Q = K, ΔG = 0 — the system is at equilibrium, and no net driving force remains.

ΔG° and the Equilibrium Constant

At equilibrium, ΔG° = -RT ln(K). A large negative ΔG° means a large K (products favored); a large positive ΔG° means a small K (reactants favored). This equation links thermodynamics directly to equilibrium position, letting you calculate K from ΔG° or vice versa.

Direction of Spontaneous Change

Every system tends toward the minimum free energy point, which is equilibrium — not necessarily 100% products. If a reaction starts with Q ≠ K, it shifts spontaneously toward K, releasing free energy (ΔG negative) until ΔG = 0. This explains why reactions don't always go to completion.

Key terms

ΔG = ΔG° + RT ln(Q)

Relates free energy change to reaction progress via the reaction quotient Q; used to determine spontaneity at any point in a reaction.

ΔG° = -RT ln(K)

Links standard free energy change to the equilibrium constant K; large negative ΔG° means large K (products favored).

ΔG at equilibrium

ΔG = 0 when Q = K, since the system has no net driving force to shift in either direction.

Q > K

Too much product relative to equilibrium; ΔG is positive, and the reaction shifts in reverse (toward reactants).

Q < K

Too little product relative to equilibrium; ΔG is negative, and the reaction shifts forward (toward products).

Try an AP-style question

Which equation relates ΔG° and K?

1. ΔG° = −RT ln K
2. ΔG° = RT ln K
3. ΔG° = K/RT
4. ΔG° = −nFK